Shrinking Core: Non-Isothermal Quak Foo Lee Chemical and Biological Engineering The University of British Columbia

Shrinking Core: Non- Isothermal Heat generated at reaction front, not throughout the volume In Steady State, Solve R r rcrc TsTs TfTf TcTc

T Conditions

Boundary Condition 1: r = r c Heat is generated = Heat conducted out through product layer Area

Boundary Condition 2: r = R Heat arriving by conduction = Heat removed for from within particle convection Bi -1 Can be obtained from B.C. 1

Solution Combine equations and eliminate T S to get T c -T f

Recall from Isothermal SC Model Substitute C A,c into (T c –T f ) equation

T c - T f ConductionConvection Diffusion in Product Layer Reaction Mass Transfer

Can Heat Transfer Control the Rate in Endo- and Exothermal Rxn? Consider C A,c ≈ C A,f ; initially rapid reaction a) Endothermic with poor heat transfer, heat will be consumed in reaction, and if can’t transfer heat in, T C will drop  reaction rate ↓ markedly and rate of reaction become the slow step occurring at a rate dictated by the flow of heat. b) Exothermic initial rapid reaction and with poor Q, T C will increased, then rate of reaction ↑ and eventually reach point where gaseous reactant can’t be transferred fast enough (external mass transfer or diffusion). Hence rate is limited.